Distance between 2 points and EArth

Question

How to measure the distance between two points, A and B, on Earth? We measure along a circle with a center, C, at the center of Earth. The radius of the circle is equal to the distance from C to the surface. Use the fact that Earth is a sphere of radius equal to approximately 4000 miles to solve: Choose any two cities in the same time zone, Google their latitudes and calculate the distance between the, then use Google maps to check your answer.

Answer 1

I chose the following cities

Sioux Falls (43.58 , -96.7)

Fargo (46.92, -96.7)

According to Google the distance is 237.36 mi

The angle between the cities is 3.34 degree

Arc length = angle . R

where R is the radius of earth. But for this equation to work the angle MUST be in radian.

3.34 degree = 3.34 * pi / 180 radian = 0.0583

So

Arc length = 0.0583 . 4000 miles = 233.17 miles

The arc length is the distance between the two cities. As you can see it is close to what google shows.

Note: choosing two cities with the same latitude or the same longitude simplifies the problem.